What's Wrong With Creationist Probability?

A recent international study in the journal Science by Professor Jon Miller of Michigan State University and his associates finds that a growing number of Americans do not believe in the theory of evolution.

In fact, the survey of 32 European nations and Japan reveals that only Turkey has a higher percentage of its citizens rejecting Darwin.

The author attributes the results in the United States to religious fundamentalism, inadequate science education, and partisan political maneuvering.

With regard to the latter Miller notes, "There is no major political party in Europe and Japan that uses opposition to evolution as a part of its political platform."

But there's another contributing factor to this opposition to evolution that I'd like to discuss here. It is the concerted attempt by creationists to dress up in the garb of mathematics fundamentalist claims about human origins and to focus criticism on what they take to be the minuscule probability of evolutionary development. (Even the conservative television pundit and ace biologist Ann Coulter has lent her perspicacity to this mathematical endeavor in her recent book.)

Creationists argue that the likelihood of, say, a new species of horse developing is absurdly tiny. The same, they say, is true of the development of the eye or the mechanism for blood clotting.

Creationists' Argument

A bit more specifically, the standard argument goes roughly as follows. A very long sequence of individually improbable mutations must occur in order for a species or a biological process to evolve.

If we assume these are independent events, then the probability of all of them occurring and occurring in the right order is the product of their respective probabilities, which is always an extremely tiny number.

Thus, for example, the probability of getting a 3, 2, 6, 2, and 5 when rolling a single die five times is 1/6 x 1/6 x 1/6 x 1/6 x 1/6 or 1/7,776 -- one chance in 7,776.

The much longer sequences of fortuitous events necessary for a new species or a new process to evolve leads to the minuscule numbers that creationists argue prove that evolution is so wildly improbable as to be essentially impossible.

The Flaw

This line of argument, however, is deeply flawed.

Leaving aside the issue of independent events, which is too extensive to discuss here, I note that there are always a fantastically huge number of evolutionary paths that might be taken by an organism (or a process) over time. I also note that there is only one that actually will be taken.

So if, after the fact, we observe the particular evolutionary path actually taken and then calculate the a priori probability of its being taken, we will get the minuscule probability that creationists mistakenly attach to the process as a whole.

Misunderstanding this tiny probability, they reject outright the evolutionary process.

Here's another example. We have a deck of cards before us. There are almost 10 to the 68th power -- a one with 68 zeroes after it -- orderings of the 52 cards in the deck. Any of the 52 cards might be first, any of the remaining 51 second, any of the remaining 50 third, and so on. This is a humongous number, but it's not hard to devise even everyday situations that give rise to much larger numbers.

Now if we shuffle this deck of cards for a long time and then examine the particular ordering of the cards that happens to result, we would be justified in concluding that the probability of this particular ordering of the cards having occurred is approximately 1 chance in 10 to the 68th power. This certainly qualifies as minuscule.

Still, we would not be justified in concluding that the shuffles could not have possibly resulted in this particular ordering because its a priori probability is so very tiny. Some ordering had to result from the shuffling, and this one did.

Nor, of course, would we be justified in concluding that the whole process of moving from one ordering to another via shuffles is so wildly improbable as to be practically impossible.

The actual result of the shufflings will always have a minuscule probability of occurring, but, unless you're a creationist, that doesn't mean the process of obtaining the result is at all dubious.

The Science study is disturbing for many reasons, not the least of which is that there's no telling to what length the creationist trunk of the G.O.P. elephant will evolve.

Professor of mathematics at Temple University, John Allen Paulos is the author of best-selling books including "Innumeracy" and "A Mathematician Plays the Stock Market." His "Who's Counting?" column on ABCNews.com appears the first weekend of every month.